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  • 1.
    Aghapournahr, Moharram
    et al.
    Teacher Training Univ, Fac Math Sci, Tehran 15614, Iran.
    Melkersson, Leif
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Local cohomology and Serre subcategories2008In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 320, no 3, p. 1275-1287Article in journal (Refereed)
    Abstract [en]

    The membership of the local cohomology modules H-a(n) (M) of a module M in certain Serre subcategories of the category of modules is studied from below (i < n) and from above (i > n). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory in the upper range just depends on the support of the module. (C) 2008 Elsevier Inc. All rights reserved.

  • 2.
    Banda, Adson
    et al.
    Univ Zambia, Zambia.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Coherent functors and asymptotic stability2019In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 522Article in journal (Refereed)
    Abstract [en]

    Asymptotic properties of high powers of an ideal related to a coherent functor F are investigated. It is shown that when N is an artinian module the sets of attached prime ideals Att(A) F(0 :(N) a(n)) are the same for n large enough. Also it is shown that for an artinian module N if the modules F(0 :(N) a(n)) have finite length and for a finitely generated module M if the modules F(M/a(n) M) have finite length, their lengths are given by polynomials in n, for large n. When A is local it is shown that, the Betti numbers beta(i)(F(M /a(n) M)) and the Bass numbers mu(i)(F(M / a(n) M)) are given by polynomials in n for large n. (C) 2018 Elsevier Inc. All rights reserved.

  • 3.
    Costa, Antonio F
    et al.
    UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Correction: Maximal order of automorphisms of trigonal Riemann surfaces (vol 323, pg 27, 2010)2011In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 341, no 1, p. 313-314Article in journal (Refereed)
    Abstract [en]

    n/a

  • 4.
    Costa, Antonio F.
    et al.
    Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Maximal order of automorphisms of trigonal Riemann surfaces2010In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 323, no 1, p. 27-31Article in journal (Refereed)
    Abstract [en]

    In this paper we find the maximal order of an automorphism of a trigonal Riemann surface of genus g, g5. We find that this order is smaller for generic than for cyclic trigonal Riemann surfaces, showing that generic trigonal surfaces have “less symmetry” than cyclic trigonal surfaces. Finally we prove that the maximal order is attained for infinitely many genera in both the cyclic and the generic case.

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  • 5.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Reyes-Carocca, Sebastian
    Univ La Frontera, Chile.
    A note on large automorphism groups of compact Riemann surfaces2020In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 547Article in journal (Refereed)
    Abstract [en]

    Belolipetsky and Jones classified those compact Riemann surfaces of genus g admitting a large group of automorphisms of order lambda(g - 1), for each lambda amp;gt; 6, under the assumption that g - 1 is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting 5(g - 1) and 6(g - 1) automorphisms, with g - 1 a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order 3(g - 1), with g - 1 a prime number. We also provide isogeny decompositions of their Jacobian varieties. (C) 2019 Elsevier Inc. All rights reserved.

    The full text will be freely available from 2021-11-26 15:46
  • 6.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Cofiniteness with respect to ideals of dimension one2012In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 372, p. 459-462Article in journal (Refereed)
    Abstract [en]

    We prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules. The proof is based on a criterion for cofiniteness with respect to an ideal of dimension one. Namely for such ideals it suffices that the two first Ext-modules in the definition for cofiniteness are finitely generated. This criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal.

  • 7.
    Melkersson, Leif
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Modules cofinite with respect to an ideal2005In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 285, no 2, p. 649-668Article in journal (Refereed)
    Abstract [en]

    [No abstract available]

  • 8.
    Thorén, Jesper
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Finite-dimensional modules of quantum affine algebras2004In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 272, no 2, p. 581-613Article in journal (Refereed)
    Abstract [en]

    We construct finite-dimensional representations of the quantum affine algebra associated to the affine Lie algebra sl2. We define an explicit action of the Drinfeld generators on the vector space tensor product of fundamental representations. The action is defined on a basis of eigenvectors for some of the generators, where the eigenvalues are the coefficients in the Laurent expansion of certain rational functions related to the Drinfeld polynomial corresponding to the module. In these modules we find a maximal submodule and by studying the quotient, we get an explicit description of all finite-dimensional irreducible representations corresponding to Drinfeld polynomials with distinct zeroes. We then describe the associated trigonometric solutions of the quantum Yang-Baxter equation. © 2004 Elsevier Inc. All rights reserved.

  • 9.
    Tkachev, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    A correction of the decomposability result in a paper by Meyer-Neutsch2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 504, p. 432-439Article in journal (Refereed)
    Abstract [en]

    In their paper of 1993, Meyer and Neutsch established the existence of a 48-dimensional associative subalgebra in the Griess algebra G. By exhibiting an explicit counter example, the present paper shows a gap in the proof one of the key results in Meyer and Neutsch’s paper, which states that an idempotent a in the Griess algebra is indecomposable if and only its Peirce 1-eigenspace (i.e. the 1-eigenspace of the linear transformation L : x → ax) is one-dimensional. The present paper fixes this gap, and shows a more general result: let V be a real commutative nonassociative algebra with an associative inner product, and let c be a nonzero idempotent of V such that its Peirce 1-eigenspace is a subalgebra; then, c is indecomposable if and only if its Peirce 1-eigenspace is one-dimensional. The proof of this result is based on a general variational argument for real commutative metrised algebras with inner product.

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  • 10.
    Tkachev, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    A Jordan algebra approach to the cubic eiconal equation2014In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 419, p. 34-51Article in journal (Refereed)
    Abstract [en]

    We establish a natural correspondence between (the equivalence classes of) cubic solutions of a cubic eiconal equation and (the isomorphy classes of) cubic Jordan algebras.

  • 11.
    Tkachev, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Addendum: A Jordan algebra approach to the cubic eiconal equation (vol 419, pg 34, 2014)2016In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 449, p. 774-774Article in journal (Other academic)
    Abstract [en]

    n/a

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